INDICADORES DE RENTABILIDAD 13

3.3.1 Introduction

The fate of the contaminants in groundwater is controlled by chemical reactions, biologi- cal or biochemical reactions, and radionuclide decay [Fetter, 1999]. Under the influence of gravity, contaminants from the point sources infiltrate further into vadose zone until they reach the water table, where they spread three-dimensionally, which is illustrated in the Figures 3.3 and 3.4 [Lapworth et al., 2012; Pope and Jones., 1999; 2011]. The contaminants are transported by diffusion, advection, and dispersion mechanisms that lower the concentration of contaminant from the initial concentration and initial time at point source, which are discussed in the follow- ing sections. These transport mechanisms are controlled by the aquifer properties that were dis- cussed in section 3.1.3, and will be referred back to throughout the next sections.

Table 3. 3: Location of select contaminant sources, their plume volume, and the volume of the pure con- taminant released. This table has been reproduced from [Kehew, 2001; Mackay and Cherry, 1989].

Site Loca- tion Presumed Source Predominant Contaminants MCL (mg/L or PPM) shown in respective order to Pre- dominant Contaminants Plume Vol- ume (Liters) Contaminant Mass Dissolved in Plume as Equiva-

lent NAPL Vol- ume in Liters or 55-gal Drums Ocean City, NJ chemical plant TCE51_{; TCA}52_; PER53 0.005; 0.2;0.005 5.70E+09 15,000 (72drums) Mountain View, CA electronics

plant TCE; TCA 0.005; 0.2 6.00E+09 9800 (47 drums)

Cape Cod, MA

sewage infil- tration beds

TCE; PER; Deter- gents

0.005; 0.005;

n/a 4.00E+10 1500 (7 drums)

Traverse City, MI

aviation fuel storage

Toluene; Xylene;

Benzene 1.0; 10.0; 0.005 4.00E+08 1000 (5 drums)

Gloucester, ON, Canada special waste landfill 1,4 Dioxane; Freon 11354_{; 1,1}

DCE55 _{4.0; 0.007 1.02E+08 190 (0.9 drums)}

San Jose, CA

electronics plant

TCA; Freon 11356_;

1,1 DCE 0.2; 4.0; 0.007 5.00E+09 130 (0.6 drums)

Denver, CO Train yard airport TCE; TCA; DBCP57 0.005; 0.2; 0.0002 4.50E+09 80 (0.4 drums) 3.3.2 Diffusion

Diffusion is a molecular process of spreading contaminants through the water, which means that it does not need a hydraulic gradient to spread [Domenico and Schwartz., 1998; Fetter, 1999]. Instead, contaminants spread by a concentration gradient, or chemical potential gradient, in a medium from higher concentration to lower concentration, and the medium can be

51 _{TCE: Trichloroethylene} 52 _{TCA: 1,1,1-trichloroethane} 53 _{PER: Tetrachloroethylene} 54 _{Freon 113: 1,1,2-trichloro-1,2,2-fluoroethane} 55 _{1,1 DCE: dichloroethylene}

56 _{Freon 113: 1,1,2-trichloro-1,2,2-fluoroethane: as of February 8, 2011, its public health goal in Califor-}

nia is set to 4.0 mg/L according to Sullivan, M. (2011), Update of The Freon 113 Public Health Goal, edited by P. a. E. T. Branch, Office of Environmental Health Hazard Assessment.

gas, liquid, or solid [Walther, 2005]. Concentration gradient will keep the diffusion mechanisms working until equilibrium is reached in which the concentration (𝐶₀) – at the point source – is equal to concentration (𝐶_𝑥) – at distance x. Temperature has an effect on diffusion because if temperature increases, then the kinetic energy increases, and the diffusion of molecules acceler- ates [Robinson and Stokes, 1965]. Quantifying diffusion can be done using Fick’s 1st Law (Equation 3.13), which quantifies diffusive flux (𝐹) in one dimension [Fetter, 1999]. Diffusive flux (mass per length squared per time) is proportional to the concentration gradient (𝑑𝐶

𝑑𝑥) that

has units of mass per volume per length and diffusion coefficient (𝐷_𝐷) that has units of area per time are experimentally derived, and 𝐷_𝐷 is a function of media and temperature. [Robinson and Stokes, 1965] have determined that 𝐷_𝐷 is temperature dependant, in which 𝐷_𝐷 is 50% less when temperature drops from 25° C to 5° C.

𝑭 = −𝑫𝒅(

𝒅𝑪 𝒅𝒙)

Equation 3.13: Diffusion

Diffusion coefficients are derived for water, but they do not apply to the groundwater be- cause groundwater flows through porous medium, which slows the rate of diffusion. Therefore, to account for the porous media an effective diffusion coefficient (D*) should be used [Fetter, 1999]. In Equation 3.14, D* is a function of tortuosity (𝜔) and the diffusion coefficient (𝐷𝑑)

[Bear, 1988]. As mentioned in section 3.1.3, tortuosity (Equation 3.12) is a ratio of tortuous path to a straight path between the two points, and tortuosity in porous media is greater than 1 [Bear, 1988]. Therefore, in diffusion, the ions would have to travel a longer path (tortuous path), which is the reason effective diffusion coefficient (D*) is used instead of diffusion coefficient (𝐷_𝑑). In summary, diffusion is a movement at a molecular level by a concentration gradient in three di- mensions, and an illustration of it (in 2D) can be seen in Figures 3.3 and Figure 3.4 in which

LNAPL and DNAPL are diffusing in the subsurface. Also, diffusion applies to other contami- nants (other than NAPLs) that are dissolvable in the water. The equations used to describe diffu- sion will be represented in the ontology by datatype properties, which will be explained through- out Chapters 4 and 5.

𝑫∗ = 𝝎𝑫𝑫 Equation 3.14: Effective diffusion coefficient

3.3.3 Advection and dispersion

Advection and dispersion are inherent in a groundwater pollution problem and both occur together [Fetter, 1999]. Advection is the bulk movement of dissolved solids (contaminant) with the flowing groundwater defined by average velocity from Equation 3.11 [Domenico and

Schwartz., 1998]. Recalling the aquifer properties from section 3.1.3, advective flux is modeled in Equation 3.15 according to the formula stated by [Fetter, 1999]. Advective flux is a product of average velocity, contaminant concentration, and effective porosity, which result in advective flux units of mass per area per time [Fetter, 1999]. Basically, advective flux only accounts for solutes that moves with the mean velocity of groundwater.

𝑭𝒙 = 𝒗̅̅̅𝑪𝒏𝒙 𝒆 Equation 3.15: Advection

Mechanical dispersion is the mixing of contaminant in water, and dispersion results in a dilution of the contaminant “at the advancing edge of flow” [Fetter, 1999]. There are two types of dispersion: longitudinal dispersion and transverse dispersion [Ingebritsen et al., 2006]. Longi- tudinal dispersion occurs when contaminant mixes with the water along the direction of the flow path, and transverse dispersion occurs when contaminant mixes with the water along direction that is normal to the flow direction [Soliman et al., 1998]. Both of the dispersion mechanisms are a function of average velocity and dispersivity (α). With i being the principal direction of

flow, the following two formulas (Equations 3.16 and 3.17) apply to longitudinal and transverse coefficient of dispersivity, in which α has units of length and velocity has units of length per time [Fetter, 1999; Ingebritsen et al., 2006; Soliman et al., 1998].

𝑪𝑴𝑫_𝑳 = 𝜶_𝑳𝒗_𝒊 Equation 3.16: Coefficient of longitudinal mechanical dispersion

𝑪𝑴𝑫_𝑻= 𝜶_𝑻𝒗_𝒊 Equation 3.17: Coefficient of transverse mechanical dispersion

3.3.4 Hydrodynamic dispersion and advective dispersion

As mentioned in section 3.3.1, hydrodynamic dispersion is the key to polluting ground- water. According to [Fetter, 1999; Hiscock, 2005], molecular diffusion and mechanical disper- sion are inseparable transport mechanisms since they occur together; as a result, the two parame- ters are combined together and are called hydrodynamic dispersion, which is measured in longi- tudinal and transverse direction (Equations 3.18 and 3.19). In these equations, the product of α and 𝑣𝑖 result in units of length squared per time, and the 𝐷∗ units are length squared per time,

which results in a length squared per time for the hydrodynamic dispersion coefficient.

𝑫𝑳 = 𝜶𝑳𝒗𝒊+ 𝑫∗ Equation 3.18: Hydrodynamic dispersion coefficient

𝑫_𝑻 = 𝜶_𝑻𝒗_𝒊+ 𝑫∗ Equation 3.19: Hydrodynamic dispersion coefficient

Hydrodynamic dispersion is spreading of contaminants on a molecular level, which does not account for the contaminants that are spread by the groundwater flow. Therefore, the total mass of solute transported in the x direction is a sum of advective transport and hydrodynamic transport (Equation 3.20), which results in units of length squared per time [Fetter, 1999].

𝑭𝒙 = 𝒗𝒙𝒏𝒆𝑪 − 𝒏𝒆𝑫𝒙

𝝏𝑪 𝝏𝒙

In this section, a brief overview of contaminant transport is provided, and the equations used in this section will be converted into datatype properties in Chapters 4 and 5. In the next section, retardation is discussed, and it will be related back to the contaminant transport, which was eluded up to this point.